In a mixing bowl, combine warm water, active dry yeast, and brown sugar. Let it sit for about 5 to 10 minutes until frothy.
Once the yeast is activated, add bread flour and salt to the bowl. Mix until a dough forms, adding more flour if too sticky.
Turn the dough out onto a floured surface and knead for about 10 minutes until smooth and elastic.
Place the kneaded dough in a greased bowl, cover it, and let it rise in a warm place for about 1 hour until doubled in size.
Punch the dough down, divide it into 12 pieces, roll into balls, and poke a hole in the center to form bagels.
Place the shaped bagels on a baking sheet, cover, and let rest for another 30 minutes.
Preheat the oven to 425°F. Boil the bagels in batches for about 1 minute on each side.
Brush the bagels with the egg wash and sprinkle with everything bagel seasoning.
Bake the bagels for 20-25 minutes until golden brown, rotating the baking sheet halfway through.
Remove from the oven and cool on a rack for at least 10 minutes before slicing.